Central catadioptric image processing with geodesic metric

International audienceBecause of the distortions produced by the insertion of a mirror, catadioptric images cannot be processed similarly to classical perspective images. Now, although the equivalence between such images and spherical images is well known, the use of spherical harmonic analysis often leads to image processing methods which are more difficult to implement. In this paper, we propose to define catadioptric image processing from the geodesic metric on the unitary sphere. We show that this definition allows to adapt very simply classical image processing methods. We focus more particularly on image gradient estimation, interest point detection, and matching. More generally, the proposed approach extends traditional image processing techniques based on Euclidean metric to central catadioptric images. We show in this paper the efficiency of the approach through different experimental results and quantitative evaluations

Scale invariant line matching on the sphere

International audienceThis paper proposes a novel approach of line matching across images captured by different types of cameras, from perspective to omnidirectional ones. Based on the spherical mapping, this method utilizes spherical SIFT point features to boost line matching and searches line correspondences using an affine invariant measure of similarity. It permits to unify the commonest cameras and to process heterogeneous images with the least distortion of visual information

Reconstruction 3D de scènes dynamiques par segmentation au sens du mouvement

National audienceL'objectif de ce travail est de reconstruire les parties sta-tiques et dynamiques d'une scène 3D à l'aide d'un robot mobile équipé d'un capteur 3D. Cette reconstruction né-cessite la classification des points 3D acquis au cours du temps en point fixe et point mobile indépendamment du dé-placement du robot. Notre méthode de segmentation utilise directement les données 3D et étudie les mouvements des objets dans la scène sans hypothèse préalable. Nous déve-loppons un algorithme complet reconstruisant les parties fixes de la scène à chaque acquisition à l'aide d'un RAN-SAC qui ne requiert que 3 points pour recaler les nuages de points. La méthode a été expérimentée sur de larges scènes en extérieur. Par ailleurs, nous montrons sur les séquences tests KITTI que la prise en compte des données 3D per-met d'améliorer les approches 2D en levant les ambiguïtés dues à la perte d'une dimension dans les images. Mots-Clefs Estimation de pose, reconstruction 3D, SfM, segmentation au sens du mouvement

Production automatique de modèles tridimensionnels par numérisation 3D

La numérisation 3D telle que pratiquée aujourd'hui repose essentiellement sur les connaissances de l'opérateur qui la réalise. La qualité des résultats reste très sensible à la procédure utilisée et par conséquent aux compétences de l'opérateur. Ainsi, la numérisation manuelle est très coûteuse en ressources humaines et matérielles et son résultat dépend fortement du niveau de technicité de l'opérateur. Les solutions de numérisation les plus avancées en milieu industriel sont basées sur une approche d'apprentissage nécessitant une adaptation manuelle pour chaque pièce. Ces systèmes sont donc semi-automatiques compte tenu de l'importance de la contribution humaine pour la planification des vues.Mon projet de thèse se focalise sur la définition d'un procédé de numérisation 3D automatique et intelligente. Ce procédé est présenté sous forme d'une séquence de processus qui sont la planification de vues, la planification de trajectoires, l'acquisition et les post-traitements des données acquises. L'originalité de notre démarche de numérisation est qu'elle est générique parce qu'elle n'est pas liée aux outils et méthodes utilisés pour la réalisation des tâches liées à chaque processus. Nous avons également développé trois méthodes de planification de vues pour la numérisation d'objets sans connaissance a priori de leurs formes. Ces méthodes garantissent une indépendance des résultats par rapport au savoir-faire de l'opérateur. L'originalité de ces approches est qu'elles sont applicables à tous types de scanners. Nous avons implanté ces méthodes sur une cellule de numérisation robotisée. Nos approches assurent une reconstruction progressive et intelligente d'un large panel d'objets de différentes classes de complexité en déplaçant efficacement le scannerThe manual 3D digitization process is expensive since it requires a highly trained technician who decides about the different views needed to acquire the object model. The quality of the final result strongly depends, in addition to the complexity of the object shape, on the selected viewpoints and thus on the human expertise. Nowadays, the most developed digitization strategies in industry are based on a teaching approach in which a human operator manually determines one set of poses for the ranging device. The main drawback of this methodology is the influence of the operator's expertise. Moreover, this technique does not fulfill the high level requirement of industrial applications which require reliable, repeatable, and fast programming routines.My thesis project focuses on the definition of a procedure for automatic and intelligent 3D digitization. This procedure is presented as a sequence of processes that are essentially the view planning, the motion planning, the acquisition and the post-processing of the acquired data. The advantage of our procedure is that it is generic since it is not performed for a specific scanning system. Moreover, it is not dependent on the methods used to perform the tasks associated with each elementary process. We also developed three view planning methods to generate a complete 3D model of unknown and complex objects that we implemented on a robotic cell. Our methods enable fast and complete 3D reconstruction while moving efficiently the scanner. Additionaly, our approaches are applicable to all kinds of range sensors.DIJON-BU Doc.électronique (212319901) / SudocSudocFranceF

Modélisation et reconstruction de surfaces par supershapes et R-fonctions

Cette thèse est consacrée à la modélisation et à la reconstruction de surfaces par supershapes 3D et R-fonctions. Nous proposons deux fonctions implicites pour les supershapes. Nous étendons la littérature en modélisation géométrique en proposant une représentation de type géométrie solide constructive ou nous combinons des supershapes et des déformations globales en utilisant les R-fonctions. Nous appliquons ensuite notre méthode à la reconstruction de surfaces à partir de nuages de points 3D issus de la numérisation d'objets réels. Nous combinons les différentes supershapes reconstruites individuellement pour reconstituer l'objet final et obtenons une représentation implicite utilisée pour définir une mesure de l'erreur de reconstruction.This dissertation deals with surface modeling and surface reconstruction using supershapes and R-functions. We introduce two implicit functions for the supershapes. We propose an extension of the geometric modeling literature with a constructive solid geometry based approach that combines supershapes and global deformations through r-functions. Supershapes and r-functions are applied to reconstruct surfaces of 3D real objects. Using the previously introduced modeling technique, we combine individually reconstructed supershapes to represent the surface of the complete object. We obtain an implicit equation that is used to define the reconstruction error.DIJON-BU Sciences Economie (212312102) / SudocSudocFranceF

Road Signs Detection and Reconstruction using Gielis Curves

International audienceRoad signs are among the most important navigation tools in transportation systems. The identification of road signs in images is usually based on first detecting road signs location using color and shape information. In this paper, we introduce such a two-stage detection method. Road signs are located in images based on color segmentation, and their corresponding shape is retrieved using a unified shape representation based on Gielis curves. The contribution of our approach is the shape reconstruction method which permits to detect any common road sign shape, i.e. circle, triangle, rectangle and octagon, by a single algorithm without any training phase. Experimental results with a dataset of 130 images containing 174 road signs of various shapes, show an accurate detection and a correct shape retrieval rate of 81.01% and 80.85% respectively

Kolmogorov Superposition Theorem and its application to wavelet image decompositions

International audienceThis paper deals with the decomposition of multivariate functions into sums and compositions of monovariate functions. The global purpose of this work is to find a suitable strategy to express complex multivariate functions using simpler functions that can be analyzed using well know techniques, instead of developing complex N-dimensional tools. More precisely, most of signal processing techniques are applied in 1D or 2D and cannot easily be extended to higher dimensions. We recall that such a decomposition exists in the Kolmogorov's superposition theorem. According to this theorem, any multivariate function can be decomposed into two types of univariate functions, that are called inner and external functions. Inner functions are associated to each dimension and linearly combined to construct a hash-function that associates every point of a multidimensional space to a value of the real interval [0,1]. Every inner function is the argument for one external function. The external functions associate real values in $[0,1]$ to the image by the multivariate function of the corresponding point of the multidimensional space. Sprecher, has proved that internal functions can be used to construct space filling curves, i.e. there exists a curve that sweeps the multidimensional space and uniquely matches corresponding values into $[0,1]$. Our goal is to obtain both a new decomposition algorithm for multivariate functions (at least bi-dimensional) and adaptive space filling curves. Two strategies can be applied. Either we construct fixed internal functions to obtain space filling curves, which allows us to construct an external function such that their sums and compositions exactly correspond to the multivariate function; or the internal function is constructed by the algorithm and is adapted to the multivariate function, providing different space filling curves for different multivariate functions. We present two of the most recent constructive algorithms of monovariate functions. The first method is due to Sprecher. We provide additional explanations to the existing algorithm and present several decomposition results for gray level images. We point out the main drawback of this method: all the function parameters are fixed, so the univariate functions cannot be modified; precisely, the inner function cannot be modified and so the space filling curve. The number of layers depends on the dimension of the decomposed function. The second algorithm, proposed by Igelnik, increases the parameters flexibility, but only approximates the monovariate functions: the number of layers is variable, a neural networks optimizes the monovariate functions and the weights associated to each layer to ensure convergence to the decomposed multivariate function. We have implemented both Sprecher's and Igelnik's algorithms and present the results of the decompositions of gray level images. There are artifacts in the reconstructed images, which leads us to apply the algorithm on wavelet decomposition images. We detail the reconstruction quality and the quantity of information contained in Igelnik's network

Dynamic (de)focused projection for three-dimensional reconstruction

International audienceWe present a novel 3-D recovery method based on structured light. This method unifies depth from focus (DFF) and depth from defocus (DFD) techniques with the use of a dynamic (de)focused projection. With this approach, the image acquisition system is specifically constructed to keep a whole object sharp in all the captured images. Therefore, only the projected patterns experience different defocused deformations according to the object's depths. When the projected patterns are out of focus, their point-spread function (PSF) is assumed to follow a Gaussian distribution. The final depth is computed by the analysis of the relationship between the sets of PSFs obtained from different blurs and the variation of the object's depths. Our new depth estimation can be employed as a stand-alone strategy. It has no problem with occlusion and correspondence issues. Moreover, it handles textureless and partially reflective surfaces. The experimental results on real objects demonstrate the effective performance of our approach, providing reliable depth estimation and competitive time consumption. It uses fewer input images than DFF, and unlike DFD, it ensures that the PSF is locally unique

A robust evolutionary algorithm for the recovery of rational Gielis curves

International audienceGielis curves (GC) can represent a wide range of shapes and patterns ranging from star shapes to symmetric and asymmetric polygons, and even self intersecting curves. Such patterns appear in natural objects or phenomena, such as flowers, crystals, pollen structures, animals, or even wave propagation. Gielis curves and surfaces are an extension of Lamé curves and surfaces (superquadrics) which have benefited in the last two decades of extensive researches to retrieve their parameters from various data types, such as range images, 2D and 3D point clouds, etc. Unfortunately, the most efficient techniques for superquadrics recovery, based on deterministic methods, cannot directly be adapted to Gielis curves. Indeed, the different nature of their parameters forbids the use of a unified gradient descent approach, which requires initial pre-processings, such as the symmetry detection, and a reliable pose and scale estimation. Furthermore, even the most recent algorithms in the literature remain extremely sensitive to initialization and often fall into local minima in the presence of large missing data. We present a simple evolutionary algorithm which overcomes most of these issues and unifies all of the required operations into a single though efficient approach. The key ideas in this paper are the replacement of the potential fields used for the cost function (closed form) by the shortest Euclidean distance (SED, iterative approach), the construction of cost functions which minimize the shortest distance as well as the curve length using R-functions, and slight modifications of the evolutionary operators. We show that the proposed cost function based on SED and R-function offers the best compromise in terms of accuracy, robustness to noise, and missing data